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Context. The standard cosmological scenario predicts a hierarchical formation for galaxies. Many substructures have been found in the Galactic halo, usually identified as clumps in kinematic spaces, like the energy-angular momentum space (E − Lz), under the hypothesis that these quantities should be conserved during the interaction. If these clumps also feature different chemical abundances, such as the metallicity distribution function (MDF), these two arguments together (different kinematic and chemical properties) are often used to motivate their association with distinct and independent merger debris. Aims. The aim of this study is to explore to what extent we can couple kinematic characteristics and metallicities of stars in the Galactic halo to reconstruct the accretion history of the Milky Way (MW). In particular, we want to understand whether different clumps in the E − Lz space with different MDFs should be associated with distinct merger debris. Methods. We analysed dissipationless, self-consistent, high-resolution N-body simulations of a MW-type galaxy accreting a satellite with a mass ratio of 1:10, with different orbital parameters and different metallicity gradients, which were assigned a posteriori. Results. We confirm that accreted stars from a ∼1:10 mass ratio merger event redistribute in a wide range of E and Lz, due to the dynamical friction process, and are thus not associated with a single region. Because satellite stars with different metallicities can be deposited in different regions of the E − Lz space (on average the more metal-rich ones end up more gravitationally bound to the MW), this implies that a single accretion of ∼1:10 can manifest with different MDFs, in different regions of the E − Lz space. Conclusions. Groups of stars with different E, Lz, and metallicities may be interpreted as originating from different satellite galaxies, but our analysis shows that these interpretations are not physically motivated. In fact, as we show, the coupling of kinematic information with MDFs to reconstruct the accretion history of the MW can bias the reconstructed merger tree towards increasing the number of past accretions and decreasing the masses of the progenitor galaxies. [ABSTRACT FROM AUTHOR]

We study the properties of Lévy flights with index 0 < α < 2 at elapsed times smaller than those required for reaching the diffusive limit, and we focus on the bulk of the walkers' distribution rather than on its tails. On the basis of the analogs of the Kramers–Moyal expansion and of the Pawula theorem, we show that, for any α ≤ 2 / 3 , the bulk of the walkers' distribution occurs at wave-numbers greater than (2 / α) 1 / (2 α) ≥ 1 , and it remains non-self-similar for a time-scale longer than the Markovian time-lag of at least one order of magnitude. This result highlights the fact that for Lévy flights, the Markovianity time-lag is not the only time-scale of the process and indeed another and longer time-scale controls the transition to the familiar power-law regime in the final diffusive limit. The magnitude of this further time-scale is independent of the index α and may compromise the reliability of applications of Lévy flights to real world cases related with recurrence and transience as optimal searching, animal foraging, and site fidelity. [ABSTRACT FROM AUTHOR]

Reply to V P Shkilev. [ABSTRACT FROM AUTHOR]